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NEW YORK — A lot of American parents seem to think they don't have to worry about saving for their children's college education because the kids will get through on scholarships and grants.

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Think again, says a study being released Monday by AllianceBernstein Investments Inc., an asset management firm based in New York.

The study looked at the college saving habits and goals of parents with children under 18 and compared them with what college financial aid administrators have to say about college funding.

The study found that 87 percent of parents believe scholarships and grants will cover at least part of their children's undergraduate expenses, and nearly three-quarters think their children are "special or unique" enough to win a scholarship.

Financial aid administrators said 92 percent of parents overestimate the amount of scholarship money their children will receive.

Meanwhile, parents are not saving much on their own for their kids' educations, the study found.

"Parents with children ages 14 to 17 plan to have an average of $12,000 saved when their child reaches college age," the study found.

That would just cover the cost of one year's schooling at a four-year public college or university, according to the most recent data from the College Board, a nonprofit association based in Washington, D.C. It would fall far short of the $29,026 College Board estimate for one year at a private institution.

Jennifer DeLong, director of college savings plans for AllianceBernstein, said that instead of saving, parents are taking on debt to fund their children's educations. And they're also expecting the children to take on debt, which can make it harder for the young people to get on their feet financially after graduation.

"Parents do seem to understand the high cost of college, but they're not doing anything about it," DeLong said. "They're not considering college saving as part of their overall financial plan, they're not talking to financial advisers."

They're also not looking at opening savings accounts that can help parents accumulate money for college, including Section 529 plans. Funds invested in these state-sponsored plans, which are named for a section of the IRS code, grow tax-deferred, and withdrawals are tax-free when used for education.

AllianceBernstein is the program manager for Rhode Island-sponsored 529 plan.

James A. Boyle, president of College Parents of America, a parental support network headquartered in Arlington, Va., said that many parents are unrealistic about scholarship and grants.

"I find that parents are usually one end of the spectrum or another _ either they wrongly assume their child is so special that they're going to get scholarship offers or they wrongly assume they make too much money to get scholarship offers," he said. "The answer is usually somewhere in between."

He added that "there are only three ways to pay for college _ before, during and after." Those who save in advance are much less likely to have to reduce their lifestyles to cover expenses while a child is in school or to go into debt.

The AllianceBernstein survey of 1,358 parents was conducted by Mathew Greenwald & Associates Inc. and had a margin of error of plus or minus 2.6 percentage points.